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Trigonometric Ratios of Multiple and Submultiple Angles MATHS - Trigonometric Ratios of Multiple and Submultiple Angles

Gujarat Board (GSEB) - STD 11 Science - MATHS (GSEB - English Medium). 105 questions in this chapter.

Question types

Trigonometric Ratios of Multiple and Submultiple Angles question types

105 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

105
Questions
5
Question groups
5
Question types
Sample Questions

Trigonometric Ratios of Multiple and Submultiple Angles questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If in $\text{a}\triangle\text{ABC},\tan\text{B}+\tan\text{C}=6,$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$
  • A
    $6$
  • B
    $1$
  • ✓
    $\frac16$
  • D
    None of these

Answer: C.

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Q 2MCQ1 Mark
If $\tan\theta_1\tan\theta_2=\text{k},$ then $\frac{\cos(\theta_1-\theta_2)}{\cos(\theta_1+\theta_2)}=$
  • ✓
    $\frac{1+\text{k}}{1-\text{k}}$
  • B
    $\frac{1-\text{k}}{1+\text{k}}$
  • C
    $\frac{\text{k}+1}{\text{k}-1}$
  • D
    $\frac{\text{k}-1}{\text{k}+1}$

Answer: A.

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Q 3MCQ1 Mark
If $\text{A}-\text{B}=\frac\pi4,$ then $(1+\tan\text{A})(1-\tan\text{B})$ is equal to:
  • ✓
    2
  • B
    1
  • C
    0
  • D
    3

Answer: A.

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Q 4MCQ1 Mark
The value of $\cos^2\Big(\frac{\pi}{6}+\text{x}\Big)-\sin^2\Big(\frac\pi6-\text{x}\Big)$ is:
  • ✓
    $\frac{1}{2}\cos2\text{x}$
  • B
    $0$
  • C
    $-\frac{1}{2}\cos2\text{x}$
  • D
    $\frac12$

Answer: A.

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Q 5MCQ1 Mark
If $\tan69^\circ+\tan66^\circ-\tan69^\circ\tan66^\circ=2\text{k},$ then k =
  • A
    $-1$
  • B
    $\frac12$
  • ✓
    $\frac{-1}{2}$
  • D
    none of these

Answer: C.

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Q 10(Each question 1 marks)1 Mark
If $\text{x}\cos\theta=\text{y}\cos\Big(\theta+\frac{2\pi}{3}\Big)=\text{z}\Big(\theta+\frac{4\pi}{3}\Big),$ then write the value of $\frac{1}{\text{x}}+\frac{1}{\text{y}}+\frac{1}{\text{z}}.$
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Q 12(Each question 2 marks)2 Marks
If $\frac{\sin(\text{x}+\text{y})}{\sin(\text{x}-\text{y)}}=\frac{\text{a}+\text{b}}{\text{a}-\text{b}}$ show that $\frac{\tan\text{x}}{\tan\text{y}}=\frac{\text{a}}{\text{b}}.$
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Q 17(Each question 3 marks)3 Marks
If $\sin\text{A}=\frac{1}{2},$ $\cos\text{B}=\frac{\sqrt{3}}{2},$ where $\frac{\pi}{2}<\text{A}<\pi$ and $0<\text{B}<\frac{\pi}{2},$find the following:​$\tan{\text{(A+B)}}$​
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Q 20(Each question 3 marks)3 Marks
If $\cos\text{A}=-\frac{24}{25},$ $\cos\text{B}=-\frac{12}{13},$ where A and B both lie in second quadrant,find the value of $\sin\text{(A+B)}$.
  1. $\sin\text{(A+B)}$
  2. $\cos\text{(A+B)}$
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